Acoustic logs are routinely used in the oil and gas industry to characterize the formation around a borehole, e.g., by identifying various types of lithology (such as shale or sandstone), detecting the presence of hydrocarbons, or measuring certain geophysical properties such as stress or permeability. To acquire an acoustic log, a sonic logging tool with one or more acoustic sources and multiple receivers may be run through the borehole (e.g., on a wireline or as part of a bottom hole assembly of a drill string) to excite acoustic waves in the formation and measure the formation response with the receivers at various depths along the borehole. For each depth, the acoustic waveforms acquired by the various receivers may be processed with a semblance (or, as it is also often referred to, beamforming) method to compute a two-dimensional (e.g., time-slowness or frequency-slowness) semblance map that generally exhibits peaks corresponding to the arrivals of various types of acoustic waves (such as compressional, refracted-shear, and Stoneley waves) travelling at different apparent velocities. The identified peaks may be aggregated across depths to obtain, for each type of wave, a log of the wave velocity or slowness (which is the inverse of the velocity) as a function of depth within the borehole.
In practice, uncertainties in the identification of the peaks due to, e.g., noise levels above or signal levels below a detection threshold can result in gaps or, worse, incorrect data in the logs. For example, if a sudden change in velocity occurs, due to a change in the surrounding formation, the compressional wave velocity may not be continuously tracked with sufficient resolution, and the automated tracking method may, instead of identifying the change in velocity, jump to another signal, such as the refracted-shear-wave signal, which may henceforth be misidentified as the compressional signal. As another example, if the compressional-wave signal, which usually corresponds to the signal peak with the highest velocity, is too weak to be detectable, the peak with the highest velocity that is detectable, which may be the refracted-shear-wave peak or a peak in the noise, may be mistaken for the compressional-wave peak.